Finite Group Databasebeta

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C3×C7×D595 #38735988

order24990
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D595
unambiguous semidirect productC5⋊(C3×C7×D119)
unambiguous semidirect productC17⋊(C3×C7×D35)

Splittings

Fitting, socle, HallC3×C5×C72×C17 ⋊ C2
derivedC5×C7×C17 ⋊ C2×C3×C7
HallC5×C72×C17 ⋊ C2×C3
HallC3×C72×C17 ⋊ D5
HallC72×C17 ⋊ C3×D5
HallC3×C5×C72 ⋊ D17
HallC3×C5×C17 ⋊ C7×D7
HallC5×C72 ⋊ C3×D17
HallC3×C72 ⋊ D85
HallC5×C17 ⋊ C3×C7×D7
HallC3×C17 ⋊ C7×D35
SylowC72 ⋊ C3×D85
SylowC17 ⋊ C3×C7×D35
HallC3×C5 ⋊ C7×D119
SylowC5 ⋊ C3×C7×D119

Subgroups

subgroupG/H
center, hypercenterC3×C7D595
commutator, cosocle, hypocenterC5×C7×C17C2×C3×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C17C2
LCSG ▷ C5×C7×C17
UCSC1 ◁ C3×C7

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3570

Conjugacy classes & character table

6279 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 78);